Thanks to Henning (member of Birdforum) my slightly dodgy hypothesis has been corrected, so unfortunately no conclusions can be drawn from measuring the bill in this way as the average values are so close. I am sure Henning won't mind me quoting him here:
"You're working from the implied assumption that bill length and upper
bill depth are proportionally connected, which the original table didn't
cover. Additionally, the probabilities implied by the standard
deviation values for the individual measurements go out of the window as
soon as you apply them to the ratio of two values.
Assuming length and depth of the beak as independent, you could estimate that roughly 50% of the males have beak length-to-depth ratios between 4.17 and 3.78, and roughly 50% of the female ones between 4.35 and 3.78.
That's almost perfect overlap in the region where you measured values seem to have been, so I'm afraid it's not possible to draw any conclusions at all from this."
Maths was never my strong point, but it was worth a try!
Therefore, I am still none the wiser as to the Bempton Albatross' gender.